lean_workbook_plus_34837

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a$ , $b$ be non-negative numbers such that $a^2+kb\geq a^3+b^2$ . Prove that: \n

a^2+b^2\leq k^2+1

Where $k\in N^+.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_34837 (a b : ℝ) (k : ℕ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a^2 + k * b ≥ a^3 + b^2) : a^2 + b^2 ≤ k^2 + 1   :=  by sorry

Source